I mean, the assassination theroy would make sense. When we meet her pre-House of Wolves she's wearing a standard issue Corsair helmet, so we really couldn't get a look at her face, but I could see her helmet getting damaged, with her losing the eye in the process, and just going helmetless as a result. I could see Cayde egging her on about her looking more tough with just the eye patch as well. That might explain the "it's personal" explanation. Actually, on that note, I could see Cayde being part of the Guardian theory. The relationship of mutual respect they had is a trope in most pop culture that is earned through combat. I could easily see Cayde getting into a bet with her on knife skills, leading to her losing an eye. Petra is the kind of person that would be more mad about losing the bet than the eye, so that could also be the source of the, "don't wanna talk about it," mentality.